Preheat convection oven to 400F (200C).
In a large bowl, toss halved potatoes with 2 tbsp olive oil, 3 cloves of minced garlic, rosemary, salt, and pepper. Spread in a single layer on a parchment-lined sheet pan and roast for 30 minutes or until internal temperature reaches 210F and exterior is golden.
Season chicken breasts with oregano, thyme, salt, and pepper. Heat remaining 1 tbsp olive oil in a heavy-bottomed skillet over medium-high heat. Sear chicken for 6-8 minutes per side until the internal temperature reaches 165F. Remove chicken and tent with foil.
Deglaze the skillet with chicken broth, scraping the fond from the bottom. Add 1 cup of heavy cream and simmer for 5-7 minutes until the sauce reduces by one-third and coats the back of a spoon. Return chicken to the pan.
Bring a large pot of salted water (1% salinity) to a boil. Cook rigatoni until al dente (approximately 11-13 minutes). Reserve 1/2 cup of pasta water and drain the rest.
In a separate saucepan over medium heat, melt butter and whisk in the remaining 1.5 cups of heavy cream and remaining garlic. Simmer gently for 3 minutes.
Gradually whisk Parmesan cheese into the cream mixture until an emulsion forms and the sauce is smooth. Incorporate reserved pasta water if the consistency is too thick.
Toss the cooked rigatoni into the Alfredo sauce until fully coated.
Plate the chicken with the herb cream sauce, side the roasted potatoes, and serve alongside the Alfredo rigatoni. Garnish with fresh parsley.